Function Norms

Definition: Function norms are norm definitions applied to function spaces. Function spaces are vector spaces whose elements are functions. The most common function spaces are LpL^p spaces.

V={f(.)f:[0,1]Rs.t.01f(x)pdx<   1p<}V = \{f(.) | f: [0,1] \rightarrow \mathbb{R} s.t. \int_0^1 |f(x)|^p dx < \infty \space \space \space 1 \leq p < \infty\}

We can define norms on VV as follows:

fp:=(01f(x)pdx)1/p\|f\|_p := \left( \int_0^1 |f(x)|^p dx \right)^{1/p}

where p1p \geq 1.

Specific Cases


#EE501 - Linear Systems Theory at METU